I am manually placing dimensions on grid annotation within my Drawing Model, but I cannot seem to snap to the small extension line that extends from the grid bubble.
Yes, this is correct. Grid bubbles, as well as their extension lines, are defined as "NotSnappable", unlike the main grid lines.
This is related to the ability to dynamically zoom in and out within a 3D Model where a grid is displayed while keeping the bubbles and extension lines always in view.
For manual dimensioning purposes simply snap to the main grid lines instead with an appropriate Extension Line offset value. This is the method used by grid auto-dimensioning. Note: Take into account the Drawing's Annotation Scale value when defining your offset values.